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Ordinary difference equations (OΔE's), mostly of order two and three, are derived for the trigonometric, Jacobian elliptic, and hyperbolic functions. The results are used to derive partial difference equations (PΔE's) for simple solutions of the wave equation and three nonlinear evolutionary partial differential equations. [ABSTRACT FROM PUBLISHER]

Duffing's differential equation in its simplest form can be approximated by a variety of difference equations. It is shown how to choose a ‘best’ difference equation in the sense that the solutions of this difference equation are successive discrete exact values of the solution of the differential equation. [ABSTRACT FROM PUBLISHER]

Duffing's equation, in its simplest form, can be approximated by various non-linear difference equations. It is shown that a particular choice can be solved in closed form giving periodic solutions. [ABSTRACT FROM PUBLISHER]

In the twelve articles that are included in this January 1964 issue of "Operations Research," the largest number deal with delays and congestion characteristics of four-arm intersections, merging intersections, vehicular-controlled intersections, and the control of a sequence of synchronized signals. The remaining papers include the results of bus-following experiments, the flow reduction aspects of removing arcs in a transportation network, the economic justification for establishing runway service priorities in an air traffic control system, the mathematical characteristics of two traffic systems whose service times increase with their occupancy, and the distribution of certain measures of travel in a circular city. publication needs of authors actively engaged in the field. This publication recommendation was adopted by the Publications Committee under its chairman, Robert Machol, and an Editorial Committee was established to handle the special issue under the chairmanship of Robert M. Oliver, who also served as editor for this special issue.